A variational method for the recovery of piecewise smooth boundaries

Variational methods for visual reconstruction try to recover a piecewise smooth function together with a set of discontinuity boundaries whose total length is generally required to be minimal. This paper presents a variational method that constrains the formation of discontinuities along piecewise smooth contours and allows the localization of a set of discontinuity boundaries with explicitly marked corners and junctions. The functional to be minimized, which involves the computation of geometrical properties of the boundaries, is approximated by a sequence of functionals which admit a simple finite element discretization. Computer examples are presented to elucidate the properties of the method.